S&DS 4320/6320: Advanced Optimization Techniques (Spring 2026)

Course Description: This course covers fundamental optimization algorithms and their theoretical analysis, emphasizing convex optimization. Topics covered include gradient descent and acceleration; lower bounds; structured problems; Newton's method; and interior point methods. Prerequisites: Knowledge of linear algebra, such as MATH 2220/2250; multivariate calculus, such as MATH 1200; probability, such as S&DS 2410/5410; optimization, such as S&DS 4310/6310; and comfort with proof-based exposition and problem sets.

Instructor: Sinho Chewi (sinho.chewi@yale.edu)

References

• Lecture notes.
• [Be] A. Beck, First-order methods in optimization (2017).
• [Bu] S. Bubeck, Convex optimization: algorithms and complexity (2015).
• [N] Y. Nesterov, Lectures on convex optimization (2018).
• [NN] Y. Nesterov and A. Nemirovskii, Interior-point polynomial algorithms in convex programming (1994).

Schedule

The course meets on Tuesdays and Thursdays, 1–2.15 p.m., in Kline Tower 205. I will also be available for an hour after each class if you have any questions or if you would like to discuss. If these times do not work for you, or if you have any other concerns, please reach me via email.

For previous editions of the course, see: Sp25.

• Jan. 13 (Tuesday): Overview of the course, preliminaries on convexity and smoothness. §1
• Jan. 15 (Thursday): Gradient flow. §2

Assignments

Grades are based solely on six problem sets and one take-home final exam. Each problem set is due roughly two weeks after it is assigned, and the last problem is mandatory for students taking S&DS 6320 and extra credit for all other students. Each problem set is weighted equally with the final, so each count for 1/7 of the total grade.

Please feel free to work on the problem sets with others, but list your collaborators at the beginning of your submission. Solutions should be arrived at without the use of AI. Problem sets should be typed in LaTeX and submitted via Gradescope (the link can be found in Canvas).